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Download QR code; Print/export Download as PDF; ... Pages in category "Mathematics textbooks" The following 83 pages are in this category, out of 83 total.
In mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module, [ 1 ] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules.
Textbooks written in Pashto distributed to Afghan school children. A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners (who could be independent learners ...
Furthermore, if the free group F has rank n and the subgroup H has index e in F, then H is free of rank 1 + e(n–1). A free group of rank k clearly has subgroups of every rank less than k. Less obviously, a (nonabelian!) free group of rank at least 2 has subgroups of all countable ranks. The commutator subgroup of a free group of rank k > 1 ...
f(X) = X n + a n−1 X n−1 + ⋯ + a 0 (where f is regarded as a polynomial in E(a 0, ..., a n−1), for some indeterminates a i, E is any field, and n ≥ 5). The tensor product of fields is not usually a field. For example, a finite extension F / E of degree n is a Galois extension if and only if there is an isomorphism of F-algebras F ⊗ ...
The Saxon Math 1 to Algebra 1/2 (the equivalent of a Pre-Algebra book) curriculum [3] is designed so that students complete assorted mental math problems, learn a new mathematical concept, practice problems relating to that lesson, and solve a variety of problems. Daily practice problems include relevant questions from the current day's lesson ...
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules.
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]